It is known to perform quantitative, non-destructive evaluation of thin items such as plates and membranes though the analysis of guided Lamb wave propagation in these structures. Laser-based ultrasonic inspection of thin plates has been studied both theoretically and experimentally. A pulsed laser source can be used to generate broadband Lamb waves that are detected, after some propagation distance, with an optical probe, and phase velocity dispersion characteristics are subsequently used to determine physical or mechanical properties of the plate. Narrow bandwidth techniques have also been used to generate Lamb waves at a single phase velocity or at a single wavelength.
Lamb waves exhibit interesting behavior at specific frequencies where the group velocity vanishes while the phase velocity remains finite. This phenomenon is observed in homogeneous, isotropic materials at the minimum frequency of the first symmetric (S1) mode, and can also be observed for higher modes. The S1 mode phase velocity appears to be double-valued over a small frequency range above a minimum frequency. The upper portion of the S1 curve, above a “zero group velocity” point ZGV, is classified as part of the S2 mode which may be viewed as a “backwards wave” S2b having phase velocity and group velocity of opposite sign. The S1 mode, on the other hand, starts at the ZGV point and continues out to higher frequencies. Just above the minimum frequency, the S1 and S2b modes interfere, having very close phase velocities and near zero group velocities. Due to the fact that both modes have zero group velocity at the ZGV point, energy coupled into the plate is not transmitted away from the excitation point and a resonance, sometimes referred to as a thickness quasi-resonance, occurs. The frequency of this resonance is slightly lower (roughly 2% to 10%) than the well-known longitudinal or shear thickness resonance associated with the S2b cut-off frequency.
It has been suggested that the zero group velocity resonance be utilized for materials characterization applications. Experimenters have observed strong transmission through a plate using air coupled ultrasound transducers at the minimum frequency of the S1 mode, and have used this resonance to measure thickness variations in millimeter-scale plates.